[EM] Participation & SARC

[MIKE OSSIPOFF]

> > I'm not sure what you mean by "It is not unique how a sophisticated
> > voter...votes", but so what? The criteria that deal with
> > strategic voting don't "presume" how someone will vote.
>

>Example: Very frequently it is presumed that if Approval Voting is
>used then the voters (if they are sophisticated) vote in such a way
>that a Condorcet winner (if one exists) will always be elected.

I doubt that anyone makes that claim. Riker showed, however, that
if voters have complete information about eachother's preferences
(and maybe about eachother's actual voting), the sincere CW will
always win, regardless of what the method is. Of course that's as
true for Approval as for any method.


>If
>this presumption is true then even Approval Voting doesn't guarantee
>that a like-minded group isn't punished for going to the polls and
>voting in a sophisticated manner. The proof of this fact is very
>similar to Moulin's proof that Condorcet and participation are
>incompatible.

I don't know how that conclusion follows, and anyway, I don't
agree with the premise.

I don't say that, under all possible conditions (including
implausible, improbable conditions) voters in Approval can't
ever worsen their outcome because they showed up & voted.

But, in that regard, I make 2 claims:

1. With Approval, if a group of voters share the same
preferences and vote in the same way, and vote in a way that
could, with some configuration of the other people's votes,
produce an outcome that that group likes better than any outcome
that they could get by another way of voting, then that will
never cause their 1st choice to lose, or cause their last choice
to win, if that wouldn't have happened had they not showed up
& voted.

[In other words, Approval meets SARC].


2. Suppose the following condition holds:

P(i,j) is the probability that i & j will be the 2 frontrunners.

If P(i,k) > (j,k), then, for any additional candidate m,
P(i,m) > p(j,m).

Unless I'm mistaken, that condition ensures that there's no
incentive to "skip" in Approval. If you vote for X, then you
should also vote for everyone whom you like better than X, if
you're choosing whom to vote for so as to maximize your expectation.

When that's so, and some authors say that it would be unreasonable
to consider otherwise, then that group of voters described in
SARC, voting as SARC describes, will never worsen their outcome
by showing up to vote.

>What do you think?: How does a sophisticated voter vote if Approval
>Voting is used?

SARC merely speaks of what happens if the voter votes in a way
that could conceivably get his best possible result. I think
many people vote in that way, and will no matter what the method
is.

Approval's compliance with FBC means that in Approval there'll
never be strategic incentive to vote anyone over one's favorite.
I doubt, then, that anyone will do that in Approval. Certainly
no one will need to.

Approval's compliance with NDDC speaks of a certain drastic
strategy that a certain majority will never need in Approval.

FBC & NDDC are about what voters won't have to do. None of these
criteria make presumptions about how sophisticated voters will
vote.

Mike Ossipoff



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